The objective of this lesson is to give first grade students a concreteunderstanding of place value by providing concrete opportunities to use placevalue to practice counting, adding and subtracting using a phenomenologicalapproach.

Review numbers 0-9 and have the students practice counting various objects in the classroom from 1 to 9. Leave the numbers on the board where the students can see them.

Give each student a place value board. The board may be constructed of poster board or construction paper. The left side of the place value board (referred to as the PVB in the remainder of this paper) is blue. The right side is white.

Explain how to read the PVB. Ask the students what is on the board. When they respond that there is nothing on the board, ask them the number word fornothing. After they say "zero" tell them to read the board zero and zero, which means that there is nothing on the left (blue) side of the PVB and nothing on the right (white) side. Remind the students that we will read the PVB the same way we read a book, that is, from left to right.

Next show the students the bell. The ringing of the bell one time means add onecube to the PVB. We always place a single cube on the right side of the PVB. This side of the board is called the ones' column. Have students practice adding a cube each time the bell rings. Have them read their boards each time a cube is placed on the board. When they have nine cubes on the white side of their boards, explain that ONLY 9 cubes can go in that column. Ring the belland ask students what they will do now. Help them come to the conclusion that they will put the cubes on the blue side of the PVB after they interlock them. These 10 cubes make up one ten. Tens are placed on the blue side of theboard which is called the tens' column.

Continue the procedure of ringing the bell, allowing students to add cubes and read their boards until they appear comfortable with the routine. Next, introduce the connecting step. Students will use number flips to show the number symbol that corresponds with the number of objects shown on the board.

After the students add to 9 tens and 9 ones, they can practice subtracting thecubes in the same manner described above. When no single cubes are availablethe students will use a ten from the blue side of the PVB, take it apart to subtract a single cube and leave the nine remaining cubes on the white side of their PVB.

The final step involves recording what has been practiced. Give each studenta strip of adding machine paper that has been folded in half vertically. Clear the boards and start the adding procedure again. After the students add, flip, and read, have one student at a time put a PVB on the floor showing the number that was constructed. The boards should line up from top to bottom. After every student has had the opportunity to put a PVB on the floor, show them how to write the numbers that show on their boards. Copy the numbers showing on the boards on the strips of paper, putting the ones on the right side of the fold and the tens on the left, and underline each number as follows: 00, 01, 02 and so on.

To extend the concept of place value, give the students many different concrete objects to count on the PVB. For example, beans can be used instead of inter-locking cubes. Each time ten beans are counted, they can be placed in a small container before placing them in the tens' column. Eventually the 10 small cups filled with 10 beans will be placed in a medium sized container and put in a third column called the hundreds' column. Two overlapping PVBs will provide this third column. Instead of cubes and beans, students may practice with Pokeno chips, straws, pencils, coins and many other objects.

Performance Assessment:

Students will be able to demonstrate, on a PVB, numbers up to 9 tens and 9 ones successfully. They will be able to read and/or write the numbers from 00 to 99, indicating that 1 ten and 1 is the same as eleven, 1 ten and 2 is the same as twelve, etc.

Conclusions:

The procedure described can be extended to the hundreds, thousands, etc. forhigher grade levels. It can also be helpful in working with money concepts.